We briefly describe the standard NNHM, which can be used to address a wide range of problems and refer to [1]} for more details. In the NNHM, study-level effects are modeled using normal distributions, while heterogeneity is modeled as an additive normal variance component on a second hierarchy level. Given \(k\)  studies with their respective effects \(y_i\)  and (assumed known) sampling variances \(\sigma _i^2\) , with \(i=1,\ldots ,k\) , the goal is to infer an overall effect \(\mu \) . The \(y_i\)  are estimates of \(\mu \) , which are assumed to be normally distributed around the \(i\) th study's true effect \(\theta _i\) : \(y_i \sim \mathcal {N}(\theta _i,\sigma _i^2)\) . In random-effects meta-analysis the study level effects \(\theta _i\)  are assumed to vary normally around the overall mean \(\mu \)  with heterogeneity variance \(\tau ^2\) , i.e. \(\theta _i \sim \mathcal {N}(\mu ,\tau ^2)\) . The marginal formulation of this model is
\(y_i \sim \mathcal {N}(\mu ,\sigma _i^2 + \tau ^2),\) 
